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Making the Rounds is a puzzle in Professor Layton and the Unwound Future. The puzzle must be solved in order to progress the story.

Puzzle

US Version

A doctor needs to visit nine different hospital rooms. After studying the room numbers, she notices that she can visit all the rooms in one round. In order to do so, she must go into a room that has at least one shared digit with the room she's currently in.

Using this method, which room will she visit fifth? Circle the correct number.

UK Version

A doctor has to visit nine hospital rooms on her rounds. The numbers of the rooms she needs to visit are listed below. When checking the room numbers she notices that if she always proceeds to a room with at least one digit in common with the room she's currently in, she can visit all the rooms in one trip.

Which will be the fifth room she visits on such a trip?

Circle the correct room number.

Hints




Click a Tab to reveal the Hint.

US Version

Try listing all the digits used in all of the room numbers (there are 18 in total). How often can each digit be used?

UK Version

Look at all the digits used in every room number. How often is each digit used?

US Version

There are some digits that can only be used once. This means that if you're in a room with a number that contains one of these digits, the only room numbers you can proceed to are those that contain the other digit.

UK Version

There are some digits that are only used once. This means that if you're in a room with a number that contains one of these digits, the only room numbers you can proceed to are those that contain the other digit.

US Version

Of the nine digits used in the room numbers, the two that can only be used once in the doctor's unique round are two and seven. The rooms that contain these digits are 29 and 71. So the doctor must visit one of these rooms first and the other one last.

UK Version

Out of the nine digits, the ones that are only used once are 2 and 7. The room numbers that contain these digits are 29 and 71. You have to visit these rooms either first or last.

US Version

If the doctor starts from room 29, the order of her round will go 29, 49, 54... If she starts from 71, the order will be 71, 18, 38...

Since rooms 29 and 71 have to home at either the start or the finish of her round, the fifth room visited will always be the same.

So...which room is it?

UK Version

If you start from room 29, the order is 29-49-54.

If you start from room 71, the order is 71-18-38.

And if 29 and 71 are the start and end of your rounds...


Solution

Incorrect

US Version

Too bad!

Study the numbers closely.

UK Version

Too bad.

Look closely at the numbers.

Correct

US Version

Correct!

Room 63 is the fifth room she will visit using this unique method.

The two and seven can only be used once. The rest of the digits can be used at least twice, so the order of her round will be as shown above. Whether she starts from room 29 or 71, the fifth room visited will always be 63.

UK Version

That's right!

Room 63. The digits 2 and 7 are only used once, while the rest of the digits are used at least twice, so her route through the nine rooms is as in the image above. Whether you start from 29 or 71, the fifth room will always be 63.

UF020S

A big thanks to http://professorlayton3walkthrough.blogspot.com

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